Economic model predictive control of nonlinear process systems using empirical models

Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first principles or through system identification techniques. In industrial practice, it may be difficult in general to obtain an accurate first‐principles model of the process. Motivated by this, in the present work, Lyapunov‐based EMPC (LEMPC) is designed with a linear empirical model that allows for closed‐loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time varying economically optimal operation is considered, conditions for closed‐loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed‐loop stability and performance properties as well as significant computational advantages. © 2014 American Institute of Chemical Engineers AIChE J, 61: 816–830, 2015     

Distributed dissipative model predictive control for process networks with imperfect communication

Results are developed to ensure stability of a dissipative distributed model predictive controller in the case of structured or arbitrary failure of the controller communication network; bounded errors in the communication may similarly be handled. Stability and minimum performance of the process network is ensured by placing a dissipative trajectory constraint on each controller. This allows for the interaction effects between units to be captured in the dissipativity properties of each process, and thus, accounted for by choosing suitable dissipativity constraints for each controller. This approach is enabled by the use of quadratic difference forms as supply rates, which capture detailed dynamic system information. A case study is presented to illustrate the results. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1682–1699, 2014     

Constrained model predictive control in ball mill grinding process

Stable control of grinding process is of great importance for improvements of operation efficiency, the recovery of the valuable minerals, and significant reductions of production costs in concentration plants. Decoupled multi-loop PID controllers are usually carried out to manage to eliminate the effects of interactions among the control loops, but they generally become sluggish due to imperfect process models and a close control of the process is usually impossible in real practice. Based on its inherent decoupling scheme, model predictive control (MPC) is employed to handle such highly interacting system. For high quality requirements, a three-input three-output model of the grinding process is constructed. Constrained dynamic matrix control (DMC) is applied in an iron ore concentration plant, and operation of the process close to their optimum operating conditions is achieved. Some practical problems about the application of MPC in grinding process are presented and discussed in detail.     

An economic model predictive control approach to integrated production management and process operation

Managing production schedules and tracking time‐varying demand of certain products while optimizing process economics are subjects of central importance in industrial applications. We investigate the use of economic model predictive control (EMPC) in tracking a production schedule. Specifically, given that only a small subset of the total process state vector is typically required to track certain scheduled values, we design a novel EMPC scheme, through proper construction of the objective function and constraints, that forces specific process states to meet the production schedule and varies the rest of the process states in a way that optimizes process economic performance. Conditions under which feasibility and closed‐loop stability of a nonlinear process under such an EMPC for schedule management can be guaranteed are developed. The proposed EMPC scheme is demonstrated through a chemical process example in which the product concentration is requested to follow a certain production schedule. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1892–1906, 2017     

Application of model predictive control to the BSM1 benchmark of wastewater treatment process

Wastewater treatment processes are difficult to be controlled because of their complex and nonlinear behavior. This paper applied model predictive control (MPC) to the Benchmark Simulation Model 1 (BSM1) wastewater treatment process to maintain the effluent quality within regulations-specified limits. Good performance was achieved under steady influent characteristics, especially concerning the nitrogen-related species. In presence of influent disturbances, two approaches have been studied: the addition of a feedforward action based on the measurement of the influent flow rate; the use of nonlinear model predictive controller by addition of a penalty function. The effects of two approaches were visible on the decrease of ammonium and nitrogen concentration which were considered as being of major importance. The results show that MPC can be effectively used for control in wastewater treatment process. By comparing performances, the nonlinear model predictive control strategy with penalty function demonstrates best with small effluent quality index and acceptable aeration and pumping energy consumption.     

A dynamic programming based approach for explicit model predictive control of hybrid systems

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multi-parametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function.     

Economic model predictive control of nonlinear process systems using Lyapunov techniques

In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Real‐time economic model predictive control of nonlinear process systems

Closed‐loop stability of nonlinear systems under real‐time Lyapunov‐based economic model predictive control (LEMPC) with potentially unknown and time‐varying computational delay is considered. To address guaranteed closed‐loop stability (in the sense of boundedness of the closed‐loop state in a compact state‐space set), an implementation strategy is proposed which features a triggered evaluation of the LEMPC optimization problem to compute an input trajectory over a finite‐time prediction horizon in advance. At each sampling period, stability conditions must be satisfied for the precomputed LEMPC control action to be applied to the closed‐loop system. If the stability conditions are not satisfied, a backup explicit stabilizing controller is applied over the sampling period. Closed‐loop stability under the real‐time LEMPC strategy is analyzed and specific stability conditions are derived. The real‐time LEMPC scheme is applied to a chemical process network example to demonstrate closed‐loop stability and closed‐loop economic performance improvement over that achieved for operation at the economically optimal steady state. © 2014 American Institute of Chemical Engineers AIChE J, 61: 555–571, 2015     

非线性Hammerstein模型预测控制策略及其在pH中和过程中的应用

所有实际工业过程都包含一定程度的非线性,如pH中和过程由于其本身的强非线性是工业过程控制中具有挑战性的难题,但至今为止仍缺乏有效的非线性控制方法。将基于差分方程模型的模型预测控制策略(model predictive control,MPC)推广到包含一个静态非线性多项式函数和一个线性差分方程动态环节的非线性Hammerstein系统,详细描述了基于静态非线性多项式函数的最优控制作用求解方法,提出了一套新的非线性Hammerstein MPC 控制策略(nonlinear Hammerstein predictive control,NLHPC)。pH中和过程控制仿真和控制实验表明,NLHPC的控制结果好于工业上常用的非线性 PID(nonlinear PID,NL-PID)控制器。     

Disturbance rejection of dead-time processes using disturbance observer and model predictive control

This article mainly focuses on disturbance rejection of dead-time processes by integrating a modified disturbance observer (MDOB) with a model predictive controller (MPC). The effect caused by model mismatches is regarded as a part of the lumped disturbances. This means that the disturbances considered here include not only external disturbances, but also internal disturbances caused by model mismatches. Control structure of the proposed method includes two parts which can be designed separately. The MPC which acts as a prefilter, is employed to generate appropriate control actions such that a desired setpoint tracking response is achieved. The MDOB is employed to estimate the disturbances of the closed-loop system, and the estimation is used for feedforward compensation design to reject disturbances. Rigorous analysis of setpoint tracking and disturbance rejection properties of the closed-loop system are given in the presence of both model mismatches and external disturbances. The proposed scheme is applied to control the temperature of a simplified jacketed stirred tank heater (JSTH). Simulation results demonstrate that the proposed method possesses a better disturbance rejection performance than those of the MDOB-PI, MPC and PI methods in controlling such dead-time processes.     

Two-layer model predictive control for chemical process model with integrating controlled variables

This paper proposes an overall solution to the two-layer model predictive control (MPC) for the integrating controlled variables in the process model. The scheme includes three modules, that is, the open-loop prediction module, the steady-state target calculation (SSTC) module, and the dynamic control module. Based on the real-time output measurements and past inputs, the open-loop prediction module predicts the future outputs in the presence of disturbances. The economic optimization of SSTC is comprised of the feasibility stage and the economics stage, considering constraints of multi-priority ranks. The dynamic control module receives the steady-state targets from SSTC and calculates the control signals. The optimization problems of SSTC and dynamic control operate with the same frequency. This overall method guarantees the consistency of three modules with respect to the model, the constraints, and the targets. The simulation example illustrates that steady-state targets are adjusted dynamically after the occurrence of disturbances, and offset-free control is achieved.     

Optimization-based predictive control of a simulated moving bed process using an identified model

For optimization-based dynamic control of simulated moving bed (SMB) process, a novel control strategy based on process identification, which is an extension of the earlier work (Song et al., 2006a. Identification and predictive control of a simulated moving bed process: purity control. Chemical Engineering Science 61, 1973-1986), is proposed. A linear output prediction model is obtained by the method of subspace identification and used for the dynamic control. The controller is designed for optimizing the production cost while maintaining the specified product purities. For all of these, the average purities over one switching period of the target components in extract and raffinate streams, the reciprocal productivity and the solvent consumption are selected as output variables, while the flow rates in 1, 2, 3 and 4 are chosen as the manipulated variables. The realization of this concept is discussed and assessed on a virtual eight column SMB unit for a system following a bi-Langmuir isotherm. The identified prediction model is proven to be in good agreement with the first principles model considered as the actual SMB process. For typical control objectives encountered in actual operation, i.e., disturbance rejection and set-point tracking, it is shown that the proposed controller exhibits excellent performance, hence it is an effective tool for optimization-based control of SMB process.     

基于经济模型预测控制的金氰化浸出过程动态实时优化

针对金氰化浸出过程时间常数大、不确定性强等问题,提出了一种基于经济模型预测控制(EMPC)的动态实时优化方法。不同于传统的模型预测控制,EMPC将经济指标直接作为滚动优化的目标函数,在每个采样时刻求解滚动窗口内的最优操作序列。和稳态优化方法相比,基于EMPC的方法能保证动态最优性,提高经济收益。此外,金氰化浸出过程受随机噪声、未知参数可变等不确定性影响,提出使用扩展卡尔曼滤波(EKF),通过构造增广系统对状态变量及不确定参数进行在线同步估计,加强EMPC的准确性和可靠性。仿真结果表明,提出的EMPC+EKF策略能有效提高金氰化浸出过程的经济性能。     

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

In this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Nonlinear model predictive control of an industrial polymerization process

Nonlinear model predictive control (NMPC) is used to maintain and control polymer quality at specified production rates because the polymer quality measures have strong interacting nonlinearities with different temperatures and feed rates. Polymer quality measures that are available from the laboratory infrequently are controlled in closed-loop using a NMPC to set the temperature profile of the reactors. NMPC results in better control of polymer quality measures at different production rates as compared to using the nonlinear process model with reaction kinetics to implement offline targets for reactor temperatures.     

Stability of model predictive control with time-varying weights

In this paper, we show that the stability of constrained Model Predictive Control (MPC) systems can be guaranteed by using time-varying weights. It unifies two popular MPC algorithms with guaranteed stability - Infinite Horizon MPC and MPC with End Constraint. Use of time-varying weights may also be useful in analyzing stability properties of MPC for linear time-varying systems as well as uncertain linear systems.     

Data‐driven model predictive quality control of batch processes

The problem of driving a batch process to a specified product quality using data‐driven model predictive control (MPC) is described. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behavior until batch termination. In this work, we handle this “missing data” problem by integrating a previously developed data‐driven modeling methodology, which combines multiple local linear models with an appropriate weighting function to describe nonlinearities, with the inferential model in a MPC framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via closed‐loop simulations of a nylon‐6,6 batch polymerization process with limited measurements. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2852–2861, 2013